Inclusion Criteria:

• Locally advanced, relapsed, and/or metastatic cancer with low or minimal tumor burden which may or may not be measurable.
• Tumor histology consistent with melanoma tumor specimen positive for NY-ESO-1 expression by IHC and/or RT-PCR.
• Inadequate response,relapse, and/or unacceptable toxicity with one or more prior systemic, surgical, or radiation cancer therapies. Inadequate response is defined as having persistent disease, or if no measurable disease, having a ≥50% likelihood of recurrence despite standard treatment per investigator assessment.
• Patients with unresectable and/or metastatic melanoma with an inadequate response to anti-PD-1 MAb therapy, defined as SD or PD using RECIST criteria following at least 3 months of therapy. Patients with PD must not be symptomatic or have worsening of Eastern Cooperative Oncology Group (ECOG) performance status due to their disease progression, and cannot have new CNS lesion. Patients must also meet the lactic acid dehydrogenase (LDH), ECOG status
• ≥ 18 years of age.
• Life expectancy of ≥ 6 months per the investigator.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• ECG without evidence of clinically significant arrhythmia or ischemia.
• If female of childbearing potential (FCBP), willing to undergo pregnancy testing and agrees to use at least one highly effective or two effective contraceptive methods during the dosing period and for three months after last LV305 injection.
• If male and sexually active with a FCBP, must agree to use highly effective contraception such as latex condom during the dosing period and for three months after last LV305 injection. 
• T3, T4, free T3, and Free T4 must be collected as part of thyroid tests

Exclusion Criteria:

• Investigational therapy within 3 weeks prior to LV305 dosing.
• Prior administration of other NY-ESO-1-targeting immunotherapeutics.
• Significant immunosuppression from:
  1. Concurrent, recent (≤ 4 weeks ago) or anticipated treatment with systemic corticosteroids at any dose, or
  2. Other immunosuppressive medications such as methotrexate, cyclosporine, azathioprine (antihistamines, non-steroidal anti- inflammatory drugs and aspirin permitted) or conditions such as common variable hypogammaglobulinemia or exposures such as large field radiotherapy
• Cancer therapies, including chemotherapy, radiation, biologics or kinase inhibitors, G-CSF or GM-CSF within 3 weeks prior to the first scheduled LV305 dosing. For patients enrolled in Part 2, Site-specific Amendment, erythropoietin, G-CSF, and GM-CSF will be allowed and anti-PD-1 therapy may be given within 3 weeks if it follows their prior treatment schedule.
• Psychiatric, other medical illness or other condition that in the opinion of the PI prevents compliance with study procedures or ability to provide valid informed consent.
• Significant autoimmune disease with the exception of alopecia, vitiligo, hypothyroidism or other conditions that have never been clinically active or were transient and have completely resolved and require no ongoing therapy. For patients enrolled in Part 2 of the Site-specific Amendment with the potential to receive pembrolizumab, active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, etc.) is not considered a form of systemic treatment.
• Myocardial infarction within 6 months of study initiation, active cardiac ischemia or New York Heart Association (NYHA) Grade III or IV heart failure.
• Inadequate organ function including:
  1. Marrow: Peripheral blood leukocyte count (WBC) < 3000/mm3, absolute neutrophils count ≤ 1500/mm3, platelets < 75000/mm3, or hemoglobin < 10 gm/dL.
  2. Hepatic: alanine aminotransferase (ALT), and aspartate aminotransferase (AST) > 2.5 x ULN, total serum bilirubin > 1.5 x ULN (patients with Gilbert's Disease may be included if their total bilirubin is ≤ 3.0 mg/dL).
  3. Renal: Creatinine > 1.5x ULN.
  4. Other: INR (prothrombin time ratio) or partial thromboplastin time (PTT) >1.5 x ULN. For patients enrolled in Part 2 of the Site-specific Amendment who are receiving anti-PD-1 MAb therapy, marrow and hepatic function as defined in criteria 8a and 8b may be up to CTCAE Grade 2 if first reviewed, found to be within acceptable safety parameters for treatment with pembrolizumab, and approved by the Sponsor Medical Monitor.
• History of other cancer within 3 years (except non-melanoma cutaneous malignancies and cervical carcinoma in situ). For patients enrolled in Part 2 of the Site-specific Amendment, history of other cancer within 1 year (except non-melanoma cutaneous malignancies and cervical carcinoma in situ. Concurrent active cancers are not allowed).
• Active tuberculosis or recent (< 2 week ago) clinically significant infection or evidence of active hepatitis B, hepatitis C or HIV infection.
• Uveal melanoma or LDH >1.1 x ULN.
• Brain metastases considered unstable as:
  1. Without confirmed stability over 60 days in patients previously treated with prior surgery or radiation; OR
  2. Associated with symptoms and/or findings; OR
  3. Requiring corticosteroids or anticonvulsants in the prior 60 days
  4. If enrolled in Part 2 of the Site-specific Amendment, new, growing, or previously untreated lesions since the start of anti-PD-1 therapy.
• Pregnant, planning to become pregnant, or nursing